论文标题
部分可观测时空混沌系统的无模型预测
Propagation properties in a multi-species SIR reaction-diffusion system
论文作者
论文摘要
我们考虑了一种多物种反应扩散系统，该系统在流行病学中产生，以描述人群中疾病的几种菌株或变体的传播。我们的模型是自然的空间，多物种，是Kermack和McKendrick经典的SIR模型的扩展。首先，我们研究了解决方案的长期行为，并表明存在“通过传播”现象的“选择”：从n个菌株开始，只有我们识别的一个子集 - 我们识别的一个子集，并以我们计算的一些给定速度进行了传播和入侵空间。然后，我们获得了有关不同菌株之间竞争影响对流行病结果的竞争影响的一些定性特性。特别是，我们证明该模型的动态没有很好地表征基本繁殖数的通常概念，这与一个菌株与经典情况有很大不同。
We consider a multi-species reaction-diffusion system that arises in epidemiology to describe the spread of several strains, or variants, of a disease in a population. Our model is a natural spatial, multi-species, extension of the classical SIR model of Kermack and McKendrick. First, we study the long-time behavior of the solutions and show that there is a "selection via propagation" phenomenon: starting with N strains, only a subset of them - that we identify - propagates and invades space, with some given speeds that we compute. Then, we obtain some qualitative properties concerning the effects of the competition between the different strains on the outcome of the epidemic. In particular, we prove that the dynamic of the model is not well characterized by the usual notion of basic reproduction number, which strongly differs from the classical case with one strain.
